Projective Cross-Ratio on Hypercomplex Numbers
Abstract
The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Mobius transformations. Applications to the geometry of conic sections and Mobius-invariant metrics on the upper half-plane are also given.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.2554
- arXiv:
- arXiv:1203.2554
- Bibcode:
- 2012arXiv1203.2554B
- Keywords:
-
- Mathematics - Complex Variables;
- Mathematics - Metric Geometry;
- 51M99 (Primary) 51N25;
- 53A35;
- 51F20 (Secondary)
- E-Print:
- doi:10.1007/s00006-012-0335-7